Computing accurate Horner form approximations to special functions in finite precision arithmetic
نویسنده
چکیده
In various applications, computers are required to compute approximations to univariate elementary and special functions such as exp and arctan to modest accuracy. This paper proposes a new heuristic for automating the design of such implementations. This heuristic takes a certain restricted specification of program structure and the desired error properties as input and takes explicit account of roundoff error during evaluation.
منابع مشابه
Nonlinear Finite Element Analysis of Bending of Straight Beams Using hp-Spectral Approximations
Displacement finite element models of various beam theories have been developed using traditional finite element interpolations (i.e., Hermite cubic or equi-spaced Lagrange functions). Various finite element models of beams differ from each other in the choice of the interpolation functions used for the transverse deflection w, total rotation φ and/or shear strain γxz, or in the integral form u...
متن کاملComputing hypergeometric functions rigorously
We present an efficient implementation of hypergeometric functions in arbitraryprecision interval arithmetic. The functions 0F1, 1F1, 2F1 and 2F0 (or the Kummer U -function) are supported for unrestricted complex parameters and argument, and by extension, we cover exponential and trigonometric integrals, error functions, Fresnel integrals, incomplete gamma and beta functions, Bessel functions, ...
متن کاملAccurate Polynomial Evaluation in Floating Point Arithmetic
One of the three main processes associated with polynomials is evaluation; the two other ones being interpolation and root finding. Higham [1, chap. 5] devotes an entire chapter to polynomials and more especially to polynomial evaluation. The small backward error the Horner scheme introduce when evaluated in floating point arithmetic justifies its practical interest. It is well known that the c...
متن کاملCompensated Horner Scheme
We present a compensated Horner scheme, that is an accurate and fast algorithm to evaluate univariate polynomials in floating point arithmetic. The accuracy of the computed result is similar to the one given by the Horner scheme computed in twice the working precision. This compensated Horner scheme runs at least as fast as existing implementations producing the same output accuracy. We also pr...
متن کاملPractical continuous functions for the internal impedance of solid cylindrical conductors
Methods for calculating the internal impedance of round wires are investigated. 'Exact' calculation using Kelvin Bessel functions runs into difficulties at radio frequencies due to rounding errors in computer floating-point arithmetic. Specialist techniques (such as the use of high-precision BCD arithmetic) could be used to circumvent this problem; but for general modelling, the use of approxim...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1508.03211 شماره
صفحات -
تاریخ انتشار 2015